Optimal Adaptivity for the SUPG Finite Element Method
Provides a theoretical guarantee of optimal convergence for adaptive SUPG methods, addressing a key gap in numerical analysis for convection-dominated PDEs.
The paper proposes an adaptive mesh-refining algorithm for the SUPG finite element method for convection-dominated problems and proves that the generated solutions converge at asymptotically optimal rates.
For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators, we propose an adaptive mesh-refining algorithm for SUPG and prove that the generated SUPG solutions converge at asymptotically optimal rates towards the exact solution.